Let's solve the inequality $8q + 5 \leq 4q + 10$ for $q$.

Step 1: Subtract $4q$ from both sides.

$8q + 5 - 4q \leq 4q + 10 - 4q$ $4q + 5 \leq 10$

Step 2: Subtract 5 from both sides.

$4q + 5 - 5 \leq 10 - 5$ $4q \leq 5$

Step 3: Divide both sides by 4 to solve for $q$.

$q \leq \frac{5}{4}$

Final Answer:

The solution to the inequality is $q \leq \frac{5}{4}$.

Would you like further details on any of the steps? Here are five related questions you can explore:

1. How do you solve a linear inequality with two variables?
2. What are the rules for adding and subtracting inequalities?
3. How do you graph the solution of a linear inequality?
4. What is the difference between solving an equation and an inequality?
5. Can an inequality have multiple solutions?

Tip: When solving inequalities, remember that multiplying or dividing both sides by a negative number reverses the inequality sign.